Hypothesis 1

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Hypothesis: Perceived happiness can predict songs valence

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Resid

Homoscedasticity

Sensitivity

Fitting the model

The model seems to fit adequately well. Both the intercept and the slope coefficients are significant and the R2 = 0.1211. This can be interpreted as happiness score being able to explain 12% of the variance in the song’s valence.

Call:
lm(formula = valence ~ z_hppy, data = stand_ds)

Residuals:
     Min       1Q   Median       3Q      Max 
-0.55939 -0.20947  0.00818  0.17684  0.55637 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept) 0.526267   0.006890   76.38   <2e-16 ***
z_hppy      0.090781   0.007132   12.73   <2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.2357 on 1168 degrees of freedom
Multiple R-squared:  0.1218,    Adjusted R-squared:  0.1211 
F-statistic:   162 on 1 and 1168 DF,  p-value: < 2.2e-16

Hypothesis 2

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Hypothesis: The relationship between happiness and valence is moderated by music sophistication

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Setup

To check this prediction we perform a moderation analysis. We keep the standardized version of the happiness scores because of the same reasons exposed in the simple linear regression.

Checking extra assumptions

Performing a moderation analysis implies entering the domains of the multiple linear regression (i.e. now there os more than one predictor). This means that the multicollinearity between predictors must be checked. To do so we look at the VIF values of the two predictors used, and there seems to be no multicollinearity at all.

               X   sophistication X:sophistication 
        1.004144         1.000172         1.004172 

Fitting the model

The model points at the interaction term being not significant and R2 = 0.1043. This points at our prediction not being met: the interaction is not significant and including this interaction term into the regression


Call:
lm(formula = Y ~ X + sophistication + X * sophistication)

Residuals:
     Min       1Q   Median       3Q      Max 
-0.56948 -0.20703  0.01238  0.17519  0.53605 

Coefficients:
                   Estimate Std. Error t value Pr(>|t|)    
(Intercept)       5.262e-01  6.956e-03  75.650   <2e-16 ***
X                 5.202e-02  4.413e-03  11.787   <2e-16 ***
sophistication    3.641e-05  3.944e-04   0.092    0.926    
X:sophistication -2.765e-04  2.407e-04  -1.149    0.251    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.2379 on 1166 degrees of freedom
Multiple R-squared:  0.1066,    Adjusted R-squared:  0.1043 
F-statistic: 46.36 on 3 and 1166 DF,  p-value: < 2.2e-16

Analysis and conclusion

Although the fit statistics already point at our prediction being not supported by the data, we can explore it visually. To do so we plot the valence distribution of songs at each level of happiness, for three different sophistication levels. If there was a moderation effect we would expect the direction of the relationship to change significantly in at least one of the three sophistication levels. Nevertheless, in all three plots, the relationship between valence and happiness seems identical.

Hypothesis 3

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Hypothesis: The variance in perceived happiness scores is lower among highly sophisticated participants

Sophistication spread

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Levene’s test

To check this prediction we use the Levene’s test. In doing so we compare the happiness scores variance of the ‘low’,‘mid’ and ‘high’ sophistication group for each of the 15 songs. If the test shows a significant p-value, at least one of the groups has a different variance than the others. To see exactly what group has this different variance and visualize the data, we plot the happiness score distribution for each sophistication group using a boxplot. If our prediction was supported by the data, then the dark green box (i.e. variance of the highly sophisticated participants) would be systematically smaller than the lighter green boxes (i.e. variance of the ‘mid’ and ‘low’ participants). As a final note, Levene’s test’s p-values are corrected for multiplied testing using Bonferroni’s correction.

Analysis

As we can see from the corrected Levene’s tests p-value, none of the songs groups have different variances. From visual inspection we can also see that the dark green box does not tend to be smaller than the other two.

Considerations

It could be the case that our sample has a low sophistication in general. This would mean that our ‘high’ group still has a low sophistication in absolute terms, and thus we are not able to infer anything about highly sophisticated people and variance in happiness scores. To check this we plot the music sophistication distribution in our sample. We can see here nevertheless, that sophistication levels are sufficiently spread and we can consider our sample representative enough.

Background

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Introduction

The demand for music has grown to become an important aspect of many peoples’ everyday life (Fuentes et al., 2019). Especially, the mode of music listening has shifted from only actively listening to music from time to time, to the soundtracking of daily activities. People accompany various activities with music, and it becomes an affective-practical resource. Several studies have focused on Music Emotion Recognition (MER) (Aljanaki et al. 2014). It focuses mostly on two dimensions: “valence (positive vs. negative) and arousal (quiet vs. energetic). However, the perfect MER model has not yet been found, as subjective and objective views on music often differ greatly (REF).

Research Question

This study will try to understand the measurement of valence and whether subjective and objective valence differs as much in our sample. Additionally, many studies have shown that musical sophistication has an effect on the relationship between objective and subjective musical perception (REF). We will examine whether the level of expertise in music will impact musical perception in the context of valence, leading to the following research question:

To what extent does objective valence judgement predict subjective happiness ratings and to what extent is this relationship moderated by music sophistication?

Data cleaning

The original data set contained 103 responses, but some had to be dropped. 21 participants did not finish the questionnaire and were thus removed from the data set. Furthermore, four participants took less than four minutes to complete the questionnaire. This was considered unreasonably low and so these responses were also removed from the data set. After this cleaning process, the data set contained 78 responses.

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Playlist

id name valence
song1 cold heart – pnau remix 0.934
song2 industry baby (feat. jack harlow) 0.892
song3 ibiza 0.880
song4 amsterdam 0.736
song5 le bled 0.598
song6 bad habits 0.537
song7 hard to say goodbye 0.418
song8 where are you now 0.262
song9 do it do it 0.637
song10 moth to a flame (with the weeknd) 0.109
song11 easy on me 0.130
song12 thunder 0.403
song13 ghost 0.473
song14 heat waves 0.531
song15 remember (and david guetta) 0.354